Popular quotes about Mathematics! Wisdom and inspiration are here!
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
Ivars PetersonMathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
George PolyaMay not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.
James Joseph SylvesterMathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don't happen to have all the data. In mathematics we have all the data, brought together in the full light of demonstration, and yet we don't understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
Simone Weil...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.
Charles Sanders PeirceThis is a wonderful book, unique and engaging. Diaconis and Graham manage to convey the awe and marvels of mathematics, and of magic tricks, especially those that depend fundamentally on mathematical ideas. They range over many delicious topics, giving us an enchanting personal view of the history and practice of magic, of mathematics, and of the fascinating connection between the two cultures. Magical Mathematics will have an utterly devoted readership.
Barry MazurLike a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.
Richard AskeyIn the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it.
Roger BaconCan the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?
Alfred RenyiThe mathematics is the odd one, odd because I'm not sure how to measure its effect. It is so fundamental to my outlook on everything and yet I'm not even sure how. It must be because in my formative years it was everything to me, the single place of beauty in my life, and of breathtaking beauty at that. I still believe that pure mathematics is the most creative thing that humanity does, though I am no longer a part of it.
Zia Haider RahmanWell, I was always... I used to get 100% in physics and chemistry and mathematics (well, maybe a couple of points off in mathematics), and that was in high school.
James DoohanWe can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.
Hans ReichenbachThe calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
John von NeumannIn mathematics I can report no deficiency, except it be that men do not sufficiently understand the excellent use of Pure Mathematics.
Francis BaconMathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.
Paul LockhartIf I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.
Alfred RenyiThe product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new.
William ThurstonOur teaching of mathematics revolves around a fundamental conflict. Rightly or wrongly, students are required to master a series of mathematical concepts and techniques, and anything that might divert them from doing so is deemed unnecessary. Putting mathematics into its cultural context, explaining what is has done for humanity, telling the story of its historical development, or pointing out the wealth of unsolved problems or even the existence of topics that do not make it into school textbooks leaves less time to prepare for the exam. So most of these things aren't discussed.
Ian Stewart[P]olitical and social and scientific values ... should be correlated in some relation of movement that could be expressed in mathematics, nor did one care in the least that all the world said it could not be done, or that one knew not enough mathematics even to figure a formula beyond the schoolboy s=(1/2)gt2. If Kepler and Newton could take liberties with the sun and moon, an obscure person ... could take liberties with Congress, and venture to multiply its attraction into the square of its time. He had only to find a value, even infinitesimal, for its attraction.
Henry AdamsThe fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
Bertrand RussellGod exists since mathematics is consistent, and the Devil exists since we cannot prove it.
Andre WeilIf a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.
Eric Temple BellWhere mathematics and spirit join, where proof of the existence of mystery-salvific mystery-shimmers just below the surfaces of human perception, experience and the linguistic veil itself, Killarney Clary's new book-her best to date-dwells, plumbs, persuades and thrills.
Jorie GrahamAll mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.
Martin GardnerIf all of mathematics disappeared, physics would be set back by exactly one week.
Richard P. FeynmanThe idea here, of course, is, you know, mathematics is the language of science, it's the way that we understand the natural world. And there's definitely been a push to sort of study advanced math and kind of reawaken the love of advanced math.
Anya KamenetzStandard mathematics has recently been rendered obsolete by the discovery that for years we have been writing the numeral five backward. This has led to reevaluation of counting as a method of getting from one to ten. Students are taught advanced concepts of Boolean algebra, and formerly unsolvable equations are dealt with by threats of reprisals.
Woody AllenWhat would mathematics have amounted to without the imagination of its devotees-its giants and their followers? There never was a discovery made without the urge of imagination-of imagination which broke the roadway through the forest in order that cold logic might follow.
David Eugene SmithIn the realm of ideas, of mental objects, those ideas whose properties are reproducible are called mathematical objects, and the study of mental objects with reproducible properties is called mathematics.
Philip J. DavisMathematics-a wonderful science, but it hasn't yet come up with a way to divide one tricycle between three small boys.
Earl WilsonOutside of mathematics and logic, there are common sense truths, such as that it is snowing that normal observers, in a specified context can agree on, subject to vagueness considerations, and theoretical truths, such as that snow is crystallised water vapour, and maybe in-between truths.
Catherine WilsonThese days people are much more aware that mathematics is a communal endeavor: even the most brilliant idea gets meaning only from its relation to the whole.
Dusa McDuffBut I simply can't stand a view limited to this earth, I feel life is so small unless it has windows into other worlds...I like mathematics largely because it is not human.
Bertrand RussellIf I ever thought of directing again, I mean - I don't know, even the idea of directing a film is a strange one for me, because I feel kind of anti mathematics in a way in that sense. Anti - I don't like when things make sense, I prefer if they don't, so if I made a film, it wouldn't make any sense and no one would see it. So maybe I'll just make little films at home with my phone, never to be released.
Johnny DeppMathematics is one of the deepest and most powerful expressions of pure human reason, and, at the same time, the most fundamental resource for description and analysis of the experiential world.
Hyman BassCryptography shifts the balance of power from those with a monopoly on violence to those who comprehend mathematics and security design.
Jacob AppelbaumUnless the chemist learns the language of mathematics, he will become a provincial and the higher branches of chemical work, that require reason as well as skill, will gradually pass out of his hands.
Alexander Crum BrownNow do you not see that the eye embraces the beauty of the whole world? It counsels and corrects all the arts of mankind... it is the prince of mathematics, and the sciences founded on it are absolutely certain. It has measured the distances and sizes of the stars it has discovered the elements and their location... it has given birth to architecture and to perspective and to the divine art of painting.
Leonardo da VinciEach generation has its few great mathematicians, and mathematics would not even notice the absence of the others. They are useful as teachers, and their research harms no one, but it is of no importance at all. A mathematician is great or he is nothing.
Alfred AdlerMathematics is fun if you don't let mathematicians push you around when you are doing it.
Jack EdmondsMathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.
Friedrich Nietzsche